So I am doing a biostats course on Stanford online, and I hit a snag. This is related to conditional probability would love it if anybody could explain the workings behind the process of the first image, which I assume is the basis for the second. The first image:: (sorry couldn't directly post it).
Anyways, here, the BC refers to the prevalence of breast cancer in a population. That probability tree basically means that .003 (.3%) has breast cancer (first event). The next branch is a conditional probability. The false-negative probability is .1 while the false positive rate is .89. I did calculate the two cases where the is a positive result, but couldn't understand the calculation in red. As much as I understand, it is the conditional probability of having breast cancer, given that a person is tested positive, but I cannot figure out how the workings come by (if that part in the red is from a formula, we haven't been taught that). Can anybody explain how that is achieved?
I believe this question is based on that concept from the first picture, but I cannot understand it. It'd be great if anyone could clear that up for me. Thanks a lot :)